Nuclear Magnetic Resonance (NMR) tools used for well-logging and downhole fluid characterization measure the response of nuclear spins in formation fluids to applied magnetic fields. Downhole NMR tools typically have a permanent magnet that produces a static magnetic field at a desired test location (e.g., where the fluid is located). The static magnetic field produces a magnetization in the fluid. The magnetization is aligned along the direction of the static field. The magnitude of the induced magnetization is proportional to the magnitude of the static field. A transmitter antenna produces a time-dependent radio frequency magnetic field that has a component perpendicular to the direction of the static field. The NMR resonance condition is satisfied when the radio frequency is equal to the Larmor frequency, which is proportional to the magnitude of the static magnetic field. The radio frequency magnetic field produces a torque on the magnetization vector that causes it to rotate about the axis of the applied radio frequency field. The rotation results in the magnetization vector developing a component perpendicular to the direction of the static magnetic field. This causes the magnetization vector to precess around the static field at the Larmor frequency. At resonance between the Larmor and transmitter frequencies, the magnetization is tipped to the transverse plane (i.e., a plane normal to the static magnetic field vector). A series of radio frequency pulses are applied to generate spin echoes that are measured with the antenna.
NMR measurements can be used to estimate, among other things, formation porosity. For example, the area under the curve of a T2 distribution for a NMR measurement can be equated to or at least provides an estimate of the NMR-based porosity. The T2 distribution may also resemble the pore size distribution in water-saturated rocks. The raw reported porosity is provided by the ratio of the initial amplitude of the raw decay and the tool response in a water tank. This porosity is independent of the lithology of the rock matrix.
It has been previously suggested to use NMR measurements with different depths of investigation (DOIs) to measure the pore pressure of tight (low permeability) formations, such as shale gas. NMR measurements are made while gas is injected into the subset of pores that are in fluid communication with the borehole through drilling-induced fractures. The data is compared with a deeper-looking NMR signal that samples pores that are not affected by the drilling-induced micro-fractures and are only in fluid communication with the borehole through the natural permeability of the formation (which is too low to allow much gas movement). Taking the deeper-looking NMR signal as a measure of the unknown gas pressure, the shallower-looking NMR signal is adjusted by varying the gas pressure in the borehole until the two measurements are equal. The known borehole gas pressure is then assumed to be equal to the unperturbed gas pressure in the formation.
The typical laboratory technique for direct permeability measurement is to flow a fluid through a formation sample, thereby inducing a pressure gradient ΔP across the sample and measuring the fluid flux q. For a fluid of unit viscosity, these quantities are related to the sample permeability, k, through Darcy's law:
                    k        =                  q                      Δ            ⁢                                                  ⁢            P                                              (        1        )            Thus, the permeability of the sample can be determined if the pressure gradient and the fluid flux are known. If the fluid is other than water, then the right hand side of Eq. (1) is multiplied by the fluid viscosity.